The lifetime of television produced by the Hishobi Company are normally distributed with a mean of 75 months and a standard deviation of 8 months. If the manufacture wants to have to replace only 1% of its televisions, what should its warranty be?

Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion and get its Z score. Insert values into equation above and solve for the score.

To determine the warranty length the Hishobi Company should offer, we need to find the value that corresponds to the 1st percentile of the normal distribution with a mean of 75 months and a standard deviation of 8 months.

To find this value, we can use a standard normal distribution table or a statistical software. However, instead of using the table or software, I will explain how to calculate it using the Z-score formula.

The Z-score formula is:
Z = (X - μ) / σ

Where:
Z = Z-score
X = Value from the data set
μ = Mean of the data set
σ = Standard deviation of the data set

In this case, the value (X) we are looking for is the warranty length, μ is the mean of 75 months, and σ is the standard deviation of 8 months. We want to find the Z-score corresponding to the 1st percentile, which means we want to find the Z-score, denoted as Z1, that corresponds to a cumulative area of 0.01 to the left of it.

Mathematically, this can be represented as:

0.01 = P(Z ≤ Z1)

To find the Z1 value, we need to find the Z-score associated with a cumulative probability of 0.01. This can be achieved by referencing a standard normal distribution table or using statistical software.

Once the Z1 value is obtained, we can rearrange the Z-score formula to solve for X, the warranty length:

X = Z1 * σ + μ

Substituting the appropriate values, we can calculate the warranty length that the Hishobi Company should offer.